Theorem A.9 (Gaussian approximation to suprema of empirical processes index by VC type classes; [1]}) 

Fix \(n \ge 1\) . Let \((\mathcal {G}_n, \vert \vert \cdot \vert \vert )\)  be a subset of a normed separable space of real functions \(f : \mathcal {X} \rightarrow \mathbb {R}\)  and is equipped with an envelope \(F_n\) . Suppose:
